President Barack Obama gave Pope Francis a box of seeds as a gift , a fitting token as their first-ever meeting provided a fresh start of sorts between the administration and Catholic leadership after years of strained relations .

`` These , I think , are carrots , '' Obama told the Pontiff , showing him a pouch from the box , which was made from timber from the first cathedral to open in the United States , in Baltimore .

The Pope gave the President two medallions -- one symbolizing the need for peace and solidarity between the two hemispheres -- and a copy of `` Evangelii Gaudium , '' or `` The Joy of the Gospel . '' The book was penned by the Pope and calls for a new era of evangelization and a renewed focus on the poor .

The tokens of goodwill underscored the goal of the meeting : Focus on areas where two of the world 's most influential men agree , and gently tread ground where they differ .

The two men greeted each other with a smile and a handshake and posed for pictures before sitting down across a table from each other . They spoke privately for nearly an hour .

When they emerged from the meeting , the President and the Vatican had slightly different takes on the tenor of their discussions , especially when it came to issues that have frayed the relationship between the Obama administration and American Catholic leaders .

'' ... -LRB- I -RRB- t was hoped that , in areas of conflict , there would be respect for humanitarian and international law and a negotiated solution between the parties involved , '' the Vatican said in a statement . `` In the context of bilateral relations and cooperation between Church and State , there was a discussion on questions of particular relevance for the Church in that country , such as the exercise of the rights to religious freedom , life and conscientious objection . ... ''

Obama , in a news conference that followed , told reporters that such issues were `` not a topic of conversation '' with the Pope and instead were discussed with Vatican Secretary of State Pietro Parolin .

According to the Vatican , the two men also discussed the issue of immigration reform and `` stated their common commitment to the eradication of human trafficking throughout the world . ''

On this point , the President and the Pope were simpatico .

`` I was grateful to have the opportunity to speak with him about the responsibilities that we all share to care for the least of these , the poor , the excluded , '' Obama told reporters after the meeting . `` And I was extremely moved by his insights about the importance of us all having a moral perspective on world problems and not simply thinking in terms of our own narrow self-interests . ''

The meeting took place two days after the U.S. Supreme Court heard arguments on a contraception mandate included in the President 's signature health care reform law .

The law exempts churches and houses of worship from the requirement , but nonprofit , religiously affiliated groups are required either to provide contraception coverage to their employees directly or through a third-party insurer .

The U.S. Conference of Catholic Bishops has been vocal in its opposition to the provision , said Sister Mary Ann Walsh , a spokeswoman for the organization .

`` Religious liberties and right-to-life issues are a concern , '' she said of the tension between American Catholic leadership and the administration . However , `` the U.S. bishops have appreciated the administration 's cooperation on issues of mutual concern . ''

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Those areas of `` mutual concern '' include immigration and poverty -- issues on which the President and the Pope could find common ground .

In an interview with the Italian newspaper Corriere della Sera , Obama pointed to the Pope 's concern for income inequality , saying , `` Given his great moral authority , when the Pope speaks it carries enormous weight . ''

Continuing to focus on income inequality , Obama said , `` And it is n't just an economic issue , it 's a moral issue . I think the Pope was speaking to the danger that over time we grow accustomed to this kind of inequality and accept it as normal . But we ca n't . ''

The President said he admires the Pope 's courage to speak out on economic and social issues .

`` It does n't mean we agree on every issue , but his voice is one that I think the world needs to hear . He challenges us , '' Obama told the newspaper . `` He implores us to remember the people , especially the poor , who are affected by the economic decisions we make . ''

Immigration issues

Francis underscored his commitment to the plight of immigrants during a trip last year to the Italian island of Lampedusa , a place where thousands of African migrants desperately fleeing political upheaval and poverty pour onto European shores . Many die in the attempt to cross .

Next month , a group of American Catholic leaders , including Cardinal Sean O'Malley , the archbishop of Boston , will follow suit and travel to the U.S.-Mexico border to highlight immigration concerns .

On Wednesday , the administration renewed its public call for immigration reform by backing an effort by House Democrats to force a vote on the matter .

`` Immigration reform is the right thing to do for our economy , our security , and our future , '' the White House said in a statement .

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Tensions between the administration and many leaders in the American Catholic community began early in the President 's tenure over his support for abortion rights .

A number of bishops criticized the University of Notre Dame 's decision in 2009 to award Obama an honorary law degree and invite him to give the commencement address .

Relations frayed further over the contraception coverage requirement in Obamacare , leading the U.S. Conference of Catholic Bishops to pan the law .

`` It was a very tough year , '' said Christopher Hale , a senior fellow with Catholics in Alliance for the Common Good who helped lead national Catholic outreach for Obama 's 2012 re-election campaign . `` It was hard to find any reasonable Catholic who thought the Health and Human Services mandate was handled well . ''

Differences over same sex-marriage only added to the strained relationship .

Seeking unity , approval

Religious experts said Francis would not have been likely to wade into politically charged conversations during the meeting .

`` The Vatican has to be very careful to not create a gap between what they 're saying and the bishops are saying , '' said Steve Schneck , director of the Institute for Policy Research and Catholic Studies at the Catholic University of America . `` They will be very careful not to undercut the American bishops in that regard . ''

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The meeting with Francis , whose approval ratings are in the high 80s , might also boost Obama in that regard . His standing with the public has hovered in the low 40s .

After all , the Pope 's name and quotes have been invoked in everything from discussions over unemployment insurance , the minimum wage and the bigger issue of income inequality .

`` If I was advising President Obama , I would say the No. 1 spokesperson on American immigration reform should be Pope Francis , '' Hale said . `` He has so much capital in this city . You have Catholics , Jews and atheists on the Hill quoting him . ''

House Speaker John Boehner , an Ohio Republican and a Catholic , recently invited the Pope to address a joint session of Congress .

`` Everybody on the planet would like to have their picture taken with the Pope these days , '' Schneck said . `` One of the things that would delight Obama is if some of that popularity would rub off . Given the President 's current low numbers , he is hoping for a bit of a boost . ''

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The meeting is called a step toward smoothing tensions with Catholics

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Abortion and Obamacare mandates on contraception are areas of disagreement

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One place for common ground : the plight of immigrants and the poor

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Pope Francis ' popularity could give President Obama a small bump in the polls